Electron-phonon coupling in the rare-earth metals

We have estimated the strength of the mass enhancement of the conduction electrons due to electron-phonon interaction in the rare metals Sc, Y, and La–Lu. The underlying self-consistent energy bands were obtained by means of the scalar relativistic linear-muffin-tin-orbital method, and the electron-phonon parameters were calculated within the Gaspari-Gyorffy formulation. For the heavier rare earths Gd–Tm spin polarization was included both in the band-structure calculations and in the treatment of the electron-phonon coupling to take into account the spin splitting of the conduction electrons induced by the 4f states. The calculated electron-phonon mass enhancement λ exhibits a pronounced variation through the series with a maximum value of 1.07 in Pr and a minimum of 0.3 in Ho. We analyze the experimental data from specific heat and de Haas–van Alphen measurements in light of the calculated electron-phonon contribution to the mass enhancement. Finally, we present for the superconducting elements Sc, Y, La, and Lu a comparison with the empirical electron-phonon coupling constants derived from the transition temperatures.